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It is well known that the mechanical material properties of a material sample after solidification are strongly tied to its microstructure structure. Nevertheless, the precise laws governing the initial stage of this structuring process, i.e. nucleation and the scenario of the successive transiental microstructure evolution, are still far from being fully understood. Here we will show that the phase-field method, which originally established itself to tackle the free boundary problem given by microstructure evolution, can also be employed to investigate the energetics of heterogeneous nucleation in a solidifying sample. Moreover it is demonstrated at the example of a generalized phase-field crystal model recently derived by the authors [R. Prieler, B. Verleye, R. Haberkern, D. Li, H. Emmerich, J. Phys. Condens. Matter, accepted for publication], how the phase-field crystal method can shade more light in open questions regarding a quantitative formulation of nucleation statistics to thereby simulate the phase transition phenomena in solidification from nucleation to crystallization in larger domains thoroughly. The aim of this contribution is to give an overview how both methods allow to study jointly nucleation from the atomic to the microscale. |
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